Some characterizations of M-tensors via digraphs

For a tensor A=(ai1⋯im)∈Cn×⋯×nA=(ai1⋯im)∈Cn×⋯×n, the associated digraph of AA has the vertex set V(A)={1,…,n}V(A)={1,…,n}, and the arc set of ΓAΓA is E(A)={(i,j)|aii2⋯im≠0,j∈{i2,…,im}≠{i,…,i}}E(A)={(i,j)|aii2⋯im≠0,j∈{i2,…,im}≠{i,…,i}}. In this paper, we give some characterizations of M-tensors and H-tensors by using the associated digraph of a tensor.